Droplet-mediated long-range interfacial correlations. Exact field theory for entropic repulsion effects

We consider near-critical two-dimensional statistical systems at phase coexistence on the half plane with boundary conditions leading to the formation of a droplet separating coexisting phases. General low-energy properties of two-dimensional field theories are used in order to find exact analytic results for one- and two-point correlation functions of both the energy density and order parameter fields. The subleading finite-size corrections are also computed and interpreted within an exact probabilistic picture in which interfacial fluctuations are characterized by the probability density of a Brownian excursion. The explicit analysis of the closed-form expression for order parameter correlations reveals the long-ranged character of interfacial correlations and their confinement within the interfacial region. The analysis of correlations is then carried out in momentum space through the notion of interface structure factor, which we extend to the case of systems bounded by a flat wall. The presence of the wall and its associated entropic repulsion leads to a specific term in the interface structure factor which we identify.

Automated summary

In this study, we investigate near-critical two-dimensional statistical systems with phase coexistence on the half plane, leading to the formation of a droplet separating the coexisting phases under specific boundary conditions. By utilizing the low-energy properties of two-dimensional field theories, exact analytical results for the one- and two-point correlation functions of both the energy density and order parameter fields are derived. Furthermore, the subleading finite-size corrections are computed and explained in the context of a precise probabilistic framework characterizing interfacial fluctuations as a probability density of a Brownian excursion. The analysis of order parameter correlations reveals the long-ranged nature of interfacial correlations and their confinement within the interfacial region. Moreover, the analysis is extended to momentum space using the concept of interface structure factor, which is also generalized to systems bounded by a flat wall, considering the presence of the wall and its associated entropic repulsion.